A coupling FEM/BEM method with linear continuous elements for acoustic-structural interaction problems

Abstract

The effects of dynamical load from acoustic waves to structural responses cannot be neglected for some cases such as a thin structure submerged in a heavy fluid. To deal with this kind of problem, a hybrid numerical method consisting of finite element method (FEM) and boundary element method (BEM) for the acoustic-structural coupling problems is proposed. The FEM is built on the first-order Reissner-Mindlin plate theory and the discrete shear gap (DSG) method is applied to construct a locking-free FEM. A collocation BEM with linear continuous element based on Burton-Miller formulation is adopted with an aim to produce a meshing conforming coupling method with the FEM not only on geometry but also on physical nodal quantities at the interface. In addition, analytical expressions of the singular integrals appeared in the Burton-Miller formulations are available to eliminate the numerical difficulties in the implementation of the BEM. Furthermore, the coupling matrix at the interface based on the conforming linear triangular mesh is obtained analytically to avoid the numerical quadrature. A solution scheme by absorbing the FEM equations to the BEM’s is proposed to take the advantage of less memory cost of the linear BEM. Optimized algorithms are designed to reduce the memory cost while keep the accuracy of the coupling method during the absorption of the structure effects to the acoustic domain. Numerical examples are setup to validate the accuracy and demonstrate the potential capability of the proposed method.